Away from all the hubbub over that other social network, how is Google+ - described by Larry Page and others as the new "social spine" of the company - doing?

As far as user numbers go, swimmingly: Page said that it has crossed the 100 million user mark. In April, Vic Gundotra said that "More than 170 million people have upgraded to Google+". That's a lot. That's more than Twitter claims as monthly active users (140 million).

But as far as user engagement goes, previous studies have said that it's not a hit. What we don't know is how many of those 170 million are active users of Google+ in the past 30 days. The suspicion, because Google has been evasive, is that the answer is: not many at all.

• The average Google+ post has less than one +1, less than one reply, and less than one re-share.

• 30% of users who make a public post never make a second one. Even after making five public posts, there is a 15% chance that a user will not post publicly again.

• Among users who make publicly-viewable posts, there is an average of 12 days between each post

• A cohort analysis reveals that, after a member makes a public post, the average number of public posts they make in each subsequent month declines steadily. This trend is not improving in newer cohorts.

The obvious question to ask of that analysis - which, as a caveat, is only made against public posts (because private posts are, well, private, and there's no way of knowing how many of them there are) - is how it compares against other social networks, partciularly Facebook, Twitter and the new kid on the block, Pinterest.

Note too that these are averages. There will be significant extremes; this is unlikely to be a normal curve. Most likely at one end there is a colossal number who don't do anything (and whose engagement may have been minimal - and perhaps nonexistent), while at the other is Robert Scoble, who never stops.

That would suggest the likely distribution of Google+ users is bathtub-shaped - high at both ends, very low in the middle. Because the people who like it really like it, as with any social network.

So how high are the ends and the middle?

Analysing the sides

The Google+ data analysing 40,000 randomly-chosen users, from RJMetrics, says that the chances are good that someone will make a second post - 70%. But, says Robert Moore, the author of the post, "after that, Google Plus does not perform as well as other social services that we have analysed. In charts like these, we typically expect to see the probability of repeat posts shoot up to well north of 90% by the time the user has made several posts. This is basically the 'once you're using it you're hooked' principle."

Cumulative average number of public posts on Google+ by length of time on the service. After eight weeks, the average is less than six. Source: RJMetrics guardian.co.uk

But instead, he says, "with Google Plus, this number never crosses the 90% mark. Even after having made five such posts, the chance of making a sixth is only 85%. That means that 15% of people who have made five posts never came back to make a sixth."

It's possible of course that the sixth is made privately - but it seems counterintuitive for someone to post publicly five times in a row and then shift entirely to private sharing.

Moore also notes that Google+ users "are less and less likely to make additional posts even a few months after initially joining."

In other words, Google+ just isn't sticky. Or, alternatively, it's attracting people who start and then go "periscope down".

But is this a pattern that's common to social networks? Not at all, he says, and contrasts it with Pinterest - which recently won an investment round valuing it at over $1bn.

Pinterest: pinteresting

It found that Pinterest was retaining and engaging users two to three times more efficiently than Twitter had been at a similar stage in its history. Over 80% of "pins" were re-pins from elsewhere on the site, indicating a lot of viral activity. (For Twitter at the same age, only 1.4% of tweets were retweets.)

But it was the user engagement that was surprising. By breaking people down into cohorts based on the months in which they joined, it could follow how active they were – with the expectation that they would drift away and become less active. But instead, the older cohort remained just as active.

"This either means that no one who starts using Pinterest ever stops or – more likely – that users who continue to use Pinterest become so much more engaged over time that their activities fully make up for those of any users who leave," Moore noted.

Of course a key point about Pinterest compared to Google+ is that Google's nascent social network is much larger, so you might not expect the same level of excitement on average. Another potential factor is that many new joiners are in effect co-opted in via their Gmail account, which "upgrades" them to Google+ whether they particularly want to or not. That's always going to degrade the level of user interaction compared to something that people actively choose to join.

Pinterest pins per user in February 2012, organised by 'cohort' of when they joined the site. The growing line indicates continued interest. Source: RJMetrics guardian.co.uk

But Pinterest users look like a determined bunch. "Between 40% and 60% of [Pinterest] users are still actively pinning even as far out as week 8," notes Moore. "This may seem like a steep dropoff, but for a consumer internet business it's exceptionally good."

And then, Twitter

And for comparison, he goes back to a Twitter analysis he did in 2009 - when the service was just three years old. I did ask Moore whether there have been any more recent analyses of Twitter; he doesn't (though might run one now).

What he found then was that Twitter decay rate - how many unique tweeters were still at it 8 weeks ahead - was down around the 20-22% mark. And also: "Once a user has tweeted once, there is a 65% chance that they will tweet again. After that second tweet, however, the chance of a third tweet goes up to 81%." And: "If someone is still tweeting in their second week as a user, it is extremely likely that they will remain on Twitter as a long-term user." Remember that this was back in 2009, when it was still part of a comparatively tiny demographic, and by his estimate had about 49 million accounts. Now that's up to 140 million, according to Twitter's release earlier this week.

But here's his conclusion on Pinterest in February: "Pinterest demonstrates some of the strongest user engagement, retention, and virality metrics I have ever seen in an online business. The company has found tremendous success among its core demographic".

Time since previous post on Google+, by number of posts. Even for those who have made 6 posts, it can be 12 days. Source: RJMetrics guardian.co.uk

OK, and now how about Google+? Less good. In fact all the metrics are less good (apart from the user numbers). On average, a user waits 15 days between making their first public post and making their second. This number declines with each subsequent post, but not drastically. There is an average of 10 days between a user's fifth and sixth public posts.

But we've already brought up the caveat about public posts, and it's entirely possible that some people make their first post in public, but after that restrict themselves to private posts, or keep posting with a constant frequency but only make their posts public occasionally. (One challenge is that it's hard, if you're a Google+ user who's in someone's circle to which they post, to know whether that post is public or not. So Google+ users themselves aren't in a great position to know this.)

Next, Moore looks at the much more public face of Google+: +1s, replies and sharing. He writes:

Of all the categories, we feel that this is the least likely to be biased by the fact that we only studied public posts. These public posts will still be visible to each member's private networks, and actually could attract +1s, shares, and replies from external users as well. If anything, we would expect our numbers here to be higher than in the general population.

Nope. From 70,000 posts, he gets • an average of 0.77 +1s per post (or, put another way, out of 10 posts, 3 won't even get the equivalent of a Facebook "Like")

• an average of 0.54 replies per post (ie, about 1 reply per two posts - no wonder people don't post; it's unrewarding)

• an average of 0.17 re-shares per post (or slightly less than 1 in 5)

I asked Moore what, of all the data about Google+, he found the most remarkable. "It's not the absence of activity that we find noteworthy here, but the drop-off," he responded. "You can speculate on the reasons why people stop posting publicly (in certain cases maybe it was a behavioural change from wanting to post publicly to wanting to post privately), but the drop-off is so consistent across the population we studied that we speculate there may be an underlying drop-off in overall activity."

He added: "I would not expect our stats on likes, +1s, and re-shares to be biased downward. Activities like these on public posts are just as visible to private circles and also can be acted upon by members of the public."

In a statement to Fast Company, which saw the study early, Google said: "By only tracking engagement on public posts, this study is flawed and not an accurate representation of all the sharing and activity taking place on Google+. As we've said before, more sharing occurs privately to circles and individuals than publicly on Google+. The beauty of Google+ is that it allows you to share privately - you don't have to publicly share your thoughts, photos or videos with the world."

Conclusion

On the plus side, pun intended, the company has clearly rethought how people may want to share and they have learned. Google+ is basically what Google Buzz should have been. However, unlike its predecessor, there's no easy way for consumers to pull in content from other networks - at least for now.

However, at least where we sit today, I believe that Google+ will leave consumers nonplussed - e.g. bewildered. While the interface is terrific and Circles and Hangouts both offer a strong value proposition, Google+ doesn't solve a consumer problem that Facebook already hasn't - or soon will - solve.